## Ray-theoretical expansion of inhomogeneous plane waves
in homogeneous isotropic elastic media

**Vaclav Vavrycuk**
### Summary

Inhomogeneous plane waves are defined as waves with an exponential
decrease of amplitude along a plane wavefront and are usually treated
in ray theory as waves with complex-valued slowness and polarization
vectors and complex rays. The inhomogeneous waves can also be treated
in real ray theory, provided higher-order ray approximations are
considered. In real ray theory, the ray expansion of the inhomogeneous
waves consists of an infinite number of terms and may converge to an
exact solution. The inhomogeneous P wave is linearly polarized in the
zero-order ray approximation and propagates with the velocity of the
homogeneous wave. Higher-order ray approximations modify and correct
the kinematic as well as dynamic attributes of the zero-order ray
solution. They produce a correct elliptical polarization of the P wave
and cause the propagation velocity to be dependent on the wave
inhomogeneity.

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In: Seismic Waves in Complex 3-D Structures, Report 17,
pp. 85-98, Dep. Geophys., Charles Univ., Prague, 2007.

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